1.3.4. Advanced operations

Section contents

1.3.4.1. Polynomials

NumPy also contains polynomials in different bases:

For example, 3x^2 + 2x - 1:

>>> p = np.poly1d([3, 2, -1])

>>> p(0)

-1

>>> p.roots

array([-1.        ,  0.33333333])

>>> p.order

2

>>> x = np.linspace(0, 1, 20)

>>> y = np.cos(x) + 0.3*np.random.rand(20)

>>> p = np.poly1d(np.polyfit(x, y, 3))



>>> t = np.linspace(0, 1, 200)

>>> plt.plot(x, y, 'o', t, p(t), '-')   

[<matplotlib.lines.Line2D object at ...>, <matplotlib.lines.Line2D object at ...>]
../../_images/sphx_glr_plot_polyfit_001.png

See http://docs.scipy.org/doc/numpy/reference/routines.polynomials.poly1d.html for more.

More polynomials (with more bases)

NumPy also has a more sophisticated polynomial interface, which supports e.g. the Chebyshev basis.

3x^2 + 2x - 1:

>>> p = np.polynomial.Polynomial([-1, 2, 3]) # coefs in different order!

>>> p(0)

-1.0

>>> p.roots()

array([-1.        ,  0.33333333])

>>> p.degree()  # In general polynomials do not always expose 'order'

2

Example using polynomials in Chebyshev basis, for polynomials in range [-1, 1]:

>>> x = np.linspace(-1, 1, 2000)

>>> y = np.cos(x) + 0.3*np.random.rand(2000)

>>> p = np.polynomial.Chebyshev.fit(x, y, 90)



>>> t = np.linspace(-1, 1, 200)

>>> plt.plot(x, y, 'r.')   

[<matplotlib.lines.Line2D object at ...>]

>>> plt.plot(t, p(t), 'k-', lw=3)   

[<matplotlib.lines.Line2D object at ...>]
../../_images/sphx_glr_plot_chebyfit_001.png

The Chebyshev polynomials have some advantages in interpolation.

1.3.4.2. Loading data files

Text files

Example: populations.txt:

# year  hare    lynx    carrot
1900    30e3    4e3     48300
1901    47.2e3  6.1e3   48200
1902    70.2e3  9.8e3   41500
1903    77.4e3  35.2e3  38200


>>> data = np.loadtxt('data/populations.txt')

>>> data    

array([[  1900.,  30000.,   4000.,  48300.],

       [  1901.,  47200.,   6100.,  48200.],

       [  1902.,  70200.,   9800.,  41500.],

...

>>> np.savetxt('pop2.txt', data)

>>> data2 = np.loadtxt('pop2.txt')

Note

If you have a complicated text file, what you can try are:

  • np.genfromtxt
  • Using Python’s I/O functions and e.g. regexps for parsing (Python is quite well suited for this)

Reminder: Navigating the filesystem with IPython

In [1]: pwd      # show current directory

'/home/user/stuff/2011-numpy-tutorial'

In [2]: cd ex

'/home/user/stuff/2011-numpy-tutorial/ex'

In [3]: ls

populations.txt  species.txt

Images

Using Matplotlib:

>>> img = plt.imread('data/elephant.png')

>>> img.shape, img.dtype

((200, 300, 3), dtype('float32'))

>>> plt.imshow(img)     

<matplotlib.image.AxesImage object at ...>

>>> plt.savefig('plot.png')



>>> plt.imsave('red_elephant.png', img[:,:,0], cmap=plt.cm.gray)
../../_images/sphx_glr_plot_elephant_001.png

This saved only one channel (of RGB):

>>> plt.imshow(plt.imread('red_elephant.png'))  

<matplotlib.image.AxesImage object at ...>
../../_images/sphx_glr_plot_elephant_002.png

Other libraries:

>>> from scipy.misc import imsave

>>> imsave('tiny_elephant.png', img[::6,::6])

>>> plt.imshow(plt.imread('tiny_elephant.png'), interpolation='nearest')  

<matplotlib.image.AxesImage object at ...>
../../_images/sphx_glr_plot_elephant_003.png

NumPy’s own format

NumPy has its own binary format, not portable but with efficient I/O:

>>> data = np.ones((3, 3))

>>> np.save('pop.npy', data)

>>> data3 = np.load('pop.npy')

Well-known (& more obscure) file formats

  • HDF5: h5py, PyTables
  • NetCDF: scipy.io.netcdf_file, netcdf4-python, …
  • Matlab: scipy.io.loadmat, scipy.io.savemat
  • MatrixMarket: scipy.io.mmread, scipy.io.mmwrite
  • IDL: scipy.io.readsav

… if somebody uses it, there’s probably also a Python library for it.

Exercise: Text data files

Write a Python script that loads data from populations.txt:: and drop the last column and the first 5 rows. Save the smaller dataset to pop2.txt.

NumPy internals

If you are interested in the NumPy internals, there is a good discussion in Advanced NumPy.